论文标题
Trised 4-manifolds上的符号形式
Symplectic forms on trisected 4-manifolds
论文作者
论文摘要
Meier和Starkston的作者以前工作表明，每个封闭的符号歧管$（x，ω）$带有理性符号形式的形式，允许与象征性拓扑兼容的三角形。在本文中，我们描述了相反的方向，并在封闭的，光滑的4-manifold $ x $的三下给出了明确的标准，该$ x $允许一个人在$ x $上构建符号结构。结合在一起，这些给出了允许合成结构的4个manifolds的新特征。这种结构通过将它们连接到4个manifolds上的符号结构的存在，分类和唯一性，激发了三维的绷紧叶子，瑟斯顿规范和接触几何的几个问题。
Previously work of the author with Meier and Starkston showed that every closed symplectic manifold $(X,ω)$ with a rational symplectic form admits a trisection compatible with the symplectic topology. In this paper, we describe the converse direction and give explicit criteria on a trisection of a closed, smooth 4-manifold $X$ that allows one to construct a symplectic structure on $X$. Combined, these give a new characterization of 4-manifolds that admit symplectic structures. This construction motivates several problems on taut foliations, the Thurston norm and contact geometry in 3-dimensions by connecting them to questions about the existence, classification and uniqueness of symplectic structures on 4-manifolds.
